This is a new project, so at this point most of our efforts have been directed at developing a detailed research proposal. As outlined in this proposal, we expect to conduct research in five areas: (1) defining general relative potency functions in the context of nonlinear dose-response models, (2) developing statistical methods for making inferences about relative potency functions, (3) strengthening inferences by borrowing information across studies, (4) combining information from multiple endpoints, and (5) assessing performance by applying these techniques to real and simulated data. These five areas of research are described in more detail below. Area 1: Within a family of chemicals having the same mode of action, the relative potency of one chemical compared to another is the ratio of their doses producing the same toxic response. The standard definition of relative potency states that this ratio is constant for all dose (or response) levels. In the context of a nonlinear dose-response model, we will relax the usual assumption that relative potency is constant and instead allow for a variable measure. This generalization is important because conventional analyses often force a constancy assumption, even when the data suggest otherwise. Speci&#64257;cally, we will consider three options by expressing log relative potency as a function of log dose, response, and fractional increase in response above baseline. Area 2: We plan to develop procedures for making con&#64257;dence statements and testing hypotheses about the relative potency function. We will assume a nonlinear model for the dose-response function and use generalized least squares methods to estimate the model parameters (and their standard errors), which in turn will be used to estimate the log relative potency function. For a given pair of chemicals, we intend to construct pointwise con&#64257;dence intervals at specific doses or responses, as well as confidence bounds for the entire log relative potency function. Also, we plan to test hypotheses about the log relative potency function being flat, and in particular zero, over certain regions. For three or more chemicals, we intend to test whether the log relative potency functions cross and whether one function dominates another over certain regions. Area 3: When dose-response data are available from multiple studies, we will extend our methods to strengthen inferences by borrowing information across studies. Specifically, if several studies of the same chemicals are performed and all involve a common endpoint, we will use techniques for hierarchical nonlinear models to incorporate random effects centered on a set of mean parameters. We will construct a log relative potency function from the mean dose-response parameters and extend our methods to make inferences about chemical-specific potencies based on the constructed log relative potency function. Area 4: Assuming a chemical exhibits toxicity through changes in several measures of response, we will investigate methods for the simultaneous analysis of multiple endpoints to assess the overall negative impact of the chemical. Many researchers are interested in how to best combine information from multiple endpoints, but presently there is no satisfactory solution. Direct application of the techniques developed for combining information over studies will not generally be applicable because different endpoints may have very different dose-response functions;thus, estimating an "average" curve will not always be appropriate. We will explore methods for defining groups of endpoints having similar dose-response patterns, for combining information within groups, and for summarizing results across groups (and assessing relative potencies across chemicals). We plan to collaborate with toxicologists to categorize endpoints and to develop a hierarchical model that nests endpoints within groups. We will also consider data-driven methods that borrow ideas from factor analysis and principal component analysis, as well as the use of expert classifications to help form prior distributions in a Bayesian analysis. Area 5: The NTP recently studied several responses to dioxin-like compounds and estimated a constant relative potency for each combination of chemical and toxicity endpoint. We plan to apply our methods to these data to estimate non-constant relative potency functions, to make confidence statements, and to test hypotheses. We intend to perform endpoint-specific analyses, as well as an analysis that combines information across endpoints. We also have dose-response data on 6 estrogenic compounds from 17 studies performed for the Organisation for Economic Co-operation and Development, all of which focused on uterine weight as the endpoint. We plan to analyze these data with the methods developed for borrowing information across studies. In addition to these analyses of real data, we will simulate data from a variety of situations, which will allow us evaluate the proposed methods in the context of knowing the true state of nature.